• Journal of the Korea Society of Computer and Information
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• v.19 no.5
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• pp.19-25
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• 2014

In this paper, I seek the chromatic number, the maximum number of colors necessary when adjoining vertices in the plane separated apart at the distance of 1 shall receive distinct colors. The upper limit of the chromatic number has been widely accepted as $4{\leq}{\chi}(G){\leq}7$ to which Hadwiger-Nelson proposed ${\chi}(G){\leq}7$ and Soifer ${\chi}(G){\leq}9$ I firstly propose an algorithm that obtains the minimum necessary chromatic number and show that ${\chi}(G)=3$ is attainable by determining the chromatic number for Hadwiger-Nelson's hexagonal graph. The proposed algorithm obtains a chromatic number of ${\chi}(G)=4$ assuming a Hadwiger-Nelson's hexagonal graph of 12 adjoining vertices, and again ${\chi}(G)=4$ for Soifer's square graph of 8 adjoining vertices. assert. Based on the results as such that this algorithm suggests the maximum chromatic number of a planar graph is ${\chi}(G)=4$ using simple assigned rule of polynomial time complexity to color for a vertex with minimum degree.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.43 no.3 s.345
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• pp.49-58
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• 2006

In this paper, a curve-fitting channel estimation method is proposed for orthogonal frequency division multiplexing (OFDM) system in a time-varying frequency-selective fading channel. The method can greatly improve channel state information (CSI) estimation accuracy by performing smoothing and interpolation through consecutive curve-fitting processes in both time domain and frequency domain. It first evaluates least-squares (LS) estimates using pilot symbols and then the estimates are approximated to a polynomial with proper degree in the LS error sense, starting from one preferred domain in which pilots we densely distributed. Smoothing, interpolation, and prediction are performed subsequently to obtain CSI estimates for data transmission. The channel estimation processes are completed by smoothing and interpolating CSI estimates in the other domain once again using the channel estimates obtained in one domain. The performance of proposed method is influenced heavily on the time variation and frequency selectivity of channel and pilot arrangement. Hence, a proper degree of polynomial and an optimum approximation interval according to various system and channel conditions are required for curve-fitting. From extensive simulation results in various channel environments, we see that the proposed method performs better than the conventional methods including the optimal Wiener filtering method, in terms of the mean square error (MSE) and bit error rate (BER).

• Journal of Sensor Science and Technology
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• v.28 no.6
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• pp.395-401
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• 2019

This paper proposes a method for estimating the location of a magnetized tip that is inside a non-transparent space or body by using arrayed giant magnetoresistance (GMR) sensors. In general, an object located in such an opaque space can be detected using X-rays, magnetic fields, ultra-sonic sensors, etc., depending on its characteristics. X-ray is mostly used for medical purposes but frequent exposure to it could cause harm to patients as well as doctors. In this study, how well a GMR sensor is applicable instead of an X-ray is investigated. The sensor's voltage output is experimentally fitted to distance with a relationship of 3rd degree polynomial. To detect a small magnetized tip with 900 Oe inside a human body, a 2×2 arrayed GMR sensor and a location estimation algorithm based on information acquired from four sensors is developed. Evaluation tests show that the suggested method is applicable to limited cases with a distance less than 33-55 mm, and the location of a magnet tip is estimated relatively well with an error less than 1.5 mm.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.467-489
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• 1994

Let $\Omega$ be a closed and bounded polygonal domain in R$^2$, or a closed line segment in R$^1$ with boundary $\Gamma$, such that there exists an invertible mapping T : $\Omega$ \longrightarrow $\Omega$ with the following correspondence: x$\in$$\Omega$ ↔ x = T(x) $\in$$\Omega$, (1.1) and (1.2) t $\in$ U$\sub$p/($\Omega$) ↔ t = to T$\^$-1/ $\in$ U$\sub$p/($\Omega$), where $\Omega$ denotes the corresponding reference elements I = [-1,1] and I ${\times}$ I in R$^1$ and R$^2$ respectively, (1.3) U$\sub$p/($\Omega$) = {t : t is a polynomial of degree $\leq$ p in each variable on $\Omega$}, and (1.4) U$\sub$p/($\Omega$) = {t : t = to T $\in$ U$\sub$p/($\Omega$)}.(omitted)

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.3
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• pp.293-300
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• 1999

The study aims to develope techniques for generating digital elevation model(DEM) from IRS-1C PAN stereo image data. The bundle adjustment technique was used to determine the satellite exterior orientation parameters as a function of along-track lines. The first degree of polynomial was selected as a function of satellite attitude and position for each scan line. To evaluate the DEM and orthoimage generated, the resulted three dimensional coordinates of the 16 elevation points were computed with the map coordinates. The elevation test showed that root mean square errors of the DEM elevation was about $\pm{16.66m}$ meters.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.621-633
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• 2024

Let R_n be the space of rational functions with prescribed poles. If r ∈ R_n, does not vanish in |z| < k, then for k = 1 $${\mid}r^{\prime}(z){\mid}{\leq}{\frac{{\mid}B^{\prime}(z){\mid}}{2}}\sup_{z{\in}T}{\mid}r(z){\mid}$$, where B(z) is the Blaschke product. In this paper, we consider a more general class of rational functions rof ∈ R_m*n, defined by (rof)(z) = r(f(z)), where f(z) is a polynomial of degree m^* and prove a more general result of the above inequality for k > 1. We also prove that $$\sup_{z{\in}T}\left[\left|{\frac{r^{*\prime}(f(z)}{B^{\prime}(z)}}\right|+\left|{\frac{r^{\prime}(f(z))}{B^{\prime}(z)}}\right|\right]=\sup_{z{\in}T}\left|{\frac{(rof)(z)}{f^{\prime}(z)}}\right|$$, and as a consequence of this result, we present a generalization of a theorem of O'Hara and Rodriguez for self-inverse polynomials. Finally, we establish a similar result when supremum is replaced by infimum for a rational function which has all its zeros in the unit circle.

• Journal of Intelligence and Information Systems
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• v.28 no.3
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• pp.105-117
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• 2022

This study analyzes the effects between stock returns and interest rate spread, difference between long-term and short-term interest rate through the polynomial linear regression analysis. The existing research concentrated on the business forecast through the interest rate spread focusing on the US market. The previous studies verified the interest rate spread based on the leading indicators of business forecast by moderating the period of long-term/short-term interest rates and analyzing the degree of leading. After the 7th reform of composite indices of business indicators in Korea of 2006, the interest rate spread was included in the items of composing the business leading indicators, which is utilized till today. Nevertheless, there are a few research on stock returns of each industry and interest rate spread in domestic stock market. Therefore, this study analyzed the stock returns of each industry and interest rate spread targeting Korean stock market. This study selected the long-term/short-term interest rates with high causality through the regression analysis, and then understood the correlations with each leading period and industry. To overcome the limitation of the simple linear regression analysis, polynomial linear regression analysis is used, which raised explanatory power. As a result, the high causality was verified when using differences between returns of corporate bond(AA-) without guarantee for three years by leading six months and call rate returns as interest rate spread. In addition, analyzing the stock returns of each industry, the relation between the relevant interest rate spread and returns of the automobile industry was the closest. This study is significant in the aspect of verifying the causality of interest rate spread, business forecast, and stock returns in Korea. Even though it could be limited to forecast the stock price by using only the interest rate spread, it would be working as a strong factor when it is properly utilized with other various factors.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.8
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• pp.35-45
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• 1999

In this paper, the addition and the multiplicative algorithm of two polynomials over finite field $GF(p^m)$ are presented. The 4-valued arithmetic processor of the serial input-parallel output modular structure on $GF(4^3)$ to be performed the presented algorithm is implemented by current mode CMOS. This 4-valued arithmetic processor using current mode CMOS is implemented one addition/multiplication selection circuit and three operation circuits; mod(4) multiplicative operation circuit, MOD operation circuit made by two mod(4) addition operation circuits, and primitive irreducible polynomial operation circuit to be performing same operation as mod(4) multiplicative operation circuit. These operation circuits are simulated under $2{\mu}m$ CMOS standard technology, $15{\mu}A$ unit current, and 3.3V VDD voltage using PSpice. The simulation results have shown the satisfying current characteristics. The presented 4-valued arithmetic processor using current mode CMOS is simple and regular for wire routing and possesses the property of modularity. Also, it is expansible for the addition and the multiplication of two polynomials on finite field increasing the degree m and suitable for VLSI implementation.

• Korean Journal of Social Welfare
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• v.35
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• pp.1-30
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• 1998

The primary objectives of this research is to identify (1) demographic and behavioral characteristics of donors for social welfare organizations in Korea and (2) factors that predicts the degrees of donors' philanthropic effort measured by the fraction of personal income given to these organizations. This study uses the data based on the responses of 191 participants among 500 donors selected randomly from the donor population of 5 major social welfare organizations. In the demographic aspect, this study showed that donors have higher frequencies in college education, Christianity, married status, age of 30s & 40s, and middle class. In the behavioral aspect, this study showed that donors have higher frequencies in inner motivation for philanthropic participation ("joy of giving"), satisfaction about the activities of social welfare organizations, trust toward funds administration of social welfare organizations, and active participation ("solicitation to others") about donation. This study also showed that donor's duration is distributed around 3 years (median) and donors' donation amount is distributed around 20,000 Won (median). This study found that the median value of donors' philanthropic effort is 1.2 percent and the distribution of philanthropic effort by income has the U shape. Finally, using polynomial regression analysis, this study found that the first power and second power of donor's income, age, continuation motivation of donation, and degree of active participation are statistically significant in predicting the degree of donors' philanthropic effort. This study will contribute to expanding knowledge about donors' characteristics and provide a practical implication for financial resource mobilization strategies in nonprofit nongovernmental sector.

• The Journal of the Korea institute of electronic communication sciences
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• v.18 no.4
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• pp.587-594
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• 2023

In this paper, we present the design and optimization process of an on-body microstrip patch antenna with a paired T-type defect for monitoring fracture recovery of human legs. This antenna is designed to be light, thin and compact despite the improvement of return loss and bandwidth performance by adjusting the size of the T-type defect. The structure around the applied human leg is structured as a 5-layer dielectric plane, and the complex dielectric constant of each layer is calculated using the 4-pole Cole-Cole model parameters. In a normal case without bone fracture, the return loss of the on-body antenna is -66.71dB at 4.0196GHz, and the return loss difference ΔS₁₁ is 37.95dB when the gallus layer have a length of 10.0mm, width of 1.0mme, and height of 2.0mm. A 3'rd degree polynomial is presented to predict the height of the gallus layer for the change in return loss, and the polynomial has a very high prediction suitability as RSS = 1.4751, R² = 0.9988246, P-value = 0.0001841.